Photonic spectrum of bichromatic optical lattices

TL;DR

This paper investigates how the photonic spectrum of a one-dimensional bichromatic optical lattice varies with atomic arrangement, revealing conditions for multiple photonic bandgaps and analyzing transmission spectra in different setups.

Contribution

It introduces a detailed analysis of the photonic spectrum in bichromatic lattices with double primitive cells, highlighting the dependence on atomic spacing ratios and experimental configurations.

Findings

Photonic bandgaps depend on the ratio of interparticle distance to lattice period.

Transmission spectra vary significantly between free space and resonator environments.

Multiple photonic bandgaps can occur in bichromatic lattices.

Abstract

We study the photonic spectrum of a one-dimensional optical lattice possessing a double primitive cell, when the atoms are well localized at the lattice minima. While a one-dimensional lattice with a simple Wigner-Seitz cell always possesses a photonic bandgap at the atomic resonance, in this configuration the photonic transmission spectrum may exhibit none, double or multiple photonic bandgaps depending on the ratio between the interparticle distance $\varrho$ inside the cell and the cell size $a$. The transmission spectra of a weak incident probe are evaluated when the atoms are trapped in free space and inside an optical resonator for realistic experimental parameters.